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Unbiased multi-index Monte Carlo
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Crisan, Dan, Moral, Pierre Del, Houssineau, Jeremie and Jasra, Ajay (2018) Unbiased multi-index Monte Carlo. Stochastic Analysis and Applications, 36 (2). pp. 257-273. doi:10.1080/07362994.2017.1394880 ISSN 1532-9356.
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Official URL: http://dx.doi.org/10.1080/07362994.2017.1394880
Abstract
We introduce a new class of Monte Carlo-based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically introduce a bias. In this paper, we show how to remove that bias, by introducing a new version of multi-index Monte Carlo (MIMC) that has the added advantage of reducing the computational effort, relative to i.i.d. sampling from the most precise discretization, for a given level of error. We cover extensions of results regarding variance and optimality criteria for the new approach. We apply the methodology to the problem of computing an unbiased mollified version of the solution of a partial differential equation with random coefficients. A second application concerns the Bayesian inference (the smoothing problem) of an infinite-dimensional signal modeled by the solution of a stochastic partial differential equation that is observed on a discrete space grid and at discrete times. Both applications are complemented by numerical simulations.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Stochastic Analysis and Applications | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 1532-9356 | ||||||||
Official Date: | 2018 | ||||||||
Dates: |
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Volume: | 36 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 257-273 | ||||||||
DOI: | 10.1080/07362994.2017.1394880 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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